Molecular rearrangement of bicyclic peroxy radicals is a key route to aerosol from aromatics

The oxidation of aromatics contributes significantly to the formation of atmospheric aerosol. Using toluene as an example, we demonstrate the existence of a molecular rearrangement channel in the oxidation mechanism. Based on both flow reactor experiments and quantum chemical calculations, we show that the bicyclic peroxy radicals (BPRs) formed in OH-initiated aromatic oxidation are much less stable than previously thought, and in the case of the toluene derived ipso-BPRs, lead to aerosol-forming low-volatility products with up to 9 oxygen atoms on sub-second timescales. Similar results are predicted for ipso-BPRs formed from many other aromatic compounds. This reaction class is likely a key route for atmospheric aerosol formation, and including the molecular rearrangement of BPRs may be vital for accurate chemical modeling of the atmosphere.

# On reaction of C6H5CD3: There is an issue of isotope effect and tunneling correction here when changing from -CH3 to -CD3. Obviously, the H-shifts here should be much faster than the D-shifts. This might be part of the reason for the low signal for C7D2H6O6 in Fig S11, and probably for C7D2H6O8 as well. Using -CD3 might underestimate the role of H shifts in Ref 35 (Wang et al., EST, 51, 8442, 2017).
# Fig S16, RONO2: BPR + NO forms ROONO first, which might decompose to RO + ONO or isomerize to RONO2. Even though barrier for rearrangement of RONO2 is lower than RO + NO2, the scheme here seems to exaggerate the role of rearrangement. RONO2s were missing in Fig S16 and Table S9. # D2O Experiments: (1) Presumably, C7H9O9 and C7D2H7O9 were from reaction of C6H5CH3, and C7D3H6O9 and C7D5H4O9 were from reaction of C6H5CD3 (Table S6). So the C7H9O9 contains only two exchangeable H-atoms, insetad "two, three and four" (Page S14). Please confirm or explain.
(2) In Fig 2, three C9H9O9 isomers were given as R3-Epo-OOH-R"O2 (containing one exchangeable H), R2b-OOH-R'2O2 (containing three exchangeable Hs), and the green C7H9O9 (lower left corner, containing two exchangeable Hs). But R2b-OOH-R'2O2 has a fast isomerization rate of ~230 s-1, and the last isomer would have a fast H shift (from the aldehyde H). Alternative isomers of C7H9O9 might be needed to account for the observed signal.
(3) Page S14, "… Fig S11 shows the time series of the normalized signals …": The figure cannot be found.
# Kinetics of R1 (as in Fig S17 and S18): It should be noticed that the two additions of O2 are both reversible, particularly for R1a-RO2 and when R1 contains excess energy. The usual "+ O2 -HO2" process in alpha-hydroxyl alkyl radicals may be limited by the 1,4 H-shift because the addition of O2 to R1a-RO2 is much less exothermic (only ~7 kcal/mol here) than the addition to normal alkyl radicals such as CH3CHOH radical (exothermic by ~30 kcal/mol). # Flow tube simulations: Could typical concentrations of OH radical and RO2 be given here? These quantities are essential in assessing the competition between unimolecular and bimolecular reactions for peroxy radicals. Reviewer #3: Remarks to the Author: This manuscripts describes a pathway in the atmospheric oxidation of aromatics that appears to be the missing link between the traditional chemistry and the unexplained HOM formation from these compounds. By combining theoretical kinetic calculations, a kinetic model, and experimental observations, the authors make a case that inclusion of this pathway leads to predictions that are consistent with the observations. The research is timely, as there is a lot of interest in HOM and aerosol formation, and the role of aromatics in urban air quality. The methodologies used are of high level and appropriate for the topic, leading to robust results. This paper describes a high-impact result that has the potential to solve a long-standing conundrum. I support publication of this manuscript.
Reviewing the experimental section is outside my field of expertise.
Most of my comments are minor, but I do have 2 main comments that I urge the authors to consider.

Main comments
To me, it feels that the authors did not do due diligence to the literature. While I recognize that space and number of references are limited in the main text, the supporting information contains extensive descriptions of mechanistic steps without any referencing at all. Most of this even seems to be based on a single paper (Wang and coworkers), which does not acknowledge the vast effort that the community has put into elucidating aromatics oxidation mechanisms to establish a base upon which the current study can to add its contribution. The paper also generalizes to aromatics beyond toluene, which is certainly not covered by a single reference to Wang et al. Reviewing the aromatics literature is daunting and I understand that this is not the manuscript to do this in full, but at the very least some key papers should be cited, as well as mechanistic reviews (e.g. Vereecken 2019, Vereecken and Francisco 2012, Atkinson 2003, Calvert 2002. These, and perhaps some additional references to SARs, will also support some of the calculations in the SI that were only done using low-level methodologies. Below, I will not list all places where literature citations are needed, as it is pervasive. One should be weary about presenting the experiments as proof of the contribution of the characterized pathway. The experiments show that an autoxidation chemistry exists, but does not establish that the molecules observed are those predicted by the theoretical analysis; autoxidation is known to generate many isomers. While the results seems consistent, there remain uncertainties on the theoretical predictions and the experimental observations, and the latter only span a small range of reaction conditions that may be insufficient to discriminate between distinct reaction mechanism. Likewise, the authors do not establish that the proposed mechanism is also consist with the observations available in the literature. Related to this is that, at first glance, the mechanism seems to miss some pathways, or at least does not discuss their contribution as far as I could find. This includes e.g. the reversibility of the epoxidation in R3 (competitive against O2 addition), the H-migration from -OOH to -O-radical in R3 (with a literature rate ~1E10 s-1), or H-scrambling and ring closure in R2b-OOH-R'2O2, all of which represent reactions classes known to be fast. The kinetic calculations also do not seem to account for the impact of fast H-scrambling across OOH/OO groups on the rate coefficient, as well-documented in the literature. It is unclear whether any of this would affect the predictions, but perhaps the mechanism is not fully robust yet.

Minor comments
p. 3 line 79: "finite timescales" define "finite", in this context probably relative to atmospheric transport time scales (regional, continental, hemisphere, global ?) p. 4 lines 90-105: This would be significantly easier to understand with a graphical inset with a Lewis-structure representation of an example. p. 5 fig 1: Top: One can not really see what the rearrangement is, due to the use of ball-and-stick graphics. See also remark above. Bottom: Perhaps an Arrhenius plot with x-axis in 1000K/T ? Then again, Nat.Comm is not a kinetics journal. p 7 fig 2: -Caption: "autoxdation" -> autoxidation -The intermediates must not be represented as trans-alkenes but strictly as cis-isomers or unspecified (where allylic rotation is possible). Trans-stereoisomers are not what was calculated (sampling a few of the log files shows as much), are not what is expected for the parent molecule decomposition, and would prevent some of the chemistry to happen (e.g. the H-shift in R2b-RO2) -The fates for P-C2 do not sum to 100% p. 9 line 183: " indicating that the mechanism proposed in this work is the dominant unimolecular pathway to the SOA precursors that we detect." "is" -> is likely to be / is consistent with / ... p. 12, fig 4 : perhaps remove the minor grid lines to lighten the plot p. 13, line 246: "This could re-initiate autoxidation and provide a long range transport mechanism for NOx" It is unclear how prompt decomposition losing NO2 could be useful for long-range NOx transport, as the NO2 is then lost before it can be transported? p. 16, wave function stability What do the CASSCF calculations show for multi-reference effects on the biradical O-O bond breaking? Is the active space (1 virtual orbital) large enough to accommodate such multi-reference effects ?
p. 17, line 341 "In the MESMER simulations, the harmonic frequencies were treated as hindered rotors" I assume the authors mean that only those internal modes corresponding to internal rotations were removed from the vibrational frequencies and treated as hindered rotors. p S9, top, ring opening in B-alkyl There are much better discussions of this channel available that should be cited, e.g. Glowacki et al. 2009, Vereecken 2018, Vereecken 2019, as well as experimental evidence of its lack of importance by the Wennberg group (Xu et al. 2020) p. S12, NO experiments. NO can lead to autoxidation proceeding through different pathways (so-called alkoxy-peroxy autoxidation steps). They may form different isomers of the same mass, and a mass spectrum won't reveal mechanistic changes. Alkoxy-peroxy autoxidation is also implicated as a key step in ring breaking HOM formation in some VOC (e.g. Shen et al. 2022, Guo et al. 2022. Furthermore, Vereecken (2018Vereecken ( , 2019 points out the role of NO in changing the early stage aromatic oxidation mechanism, based on available literature data. These experiments may thus not as straightforward to interpret as the authors imply. p. S17, top: "the rearrangement mechanism is also possible for other aromatic derived bicyclic molecules. Table S8 " Without context, it is not clear which rearrangement mechanism is meant. The bicyclic alkyl radicals have very different rearrangement mechanism reported (ring retaining with epoxide-alkoxy) than given in this work for bicyclic peroxy radicals (ring opening with H-shift and carbonyl formation).
p. S19, bottom -Mention "site-specific O2 addition" at the start of the last paragraph -"H-abstraction by O2 to form C7H8O5 is not direct but follows the initial addition of O2 to the C(OH) carbon." This needs specific literature citations -"These transition states were calculated to be -0.7 kcal/mol and 1.9 kcal/mol, respectively, above R1 at F12 level of theory." -> "...relative to R1 at the F12 level of theory." -" the potential energy surface shown in Fig. S12 was used as input in a MESMER simulation to account for the excess energy of R1." This glosses over a lot of details. At the very least refer explicitly to the Mesmer input files in the Zenodo archive, but preferable document this more thoroughly. p. S20, bottom " the analytical solution is represented by its Taylor expansion" The analytical solution to what? The MCM ? p. S21, middle "The likely reason for this is the less reactive TME RO2s." Why are they less reactive ? Is literature data available ? p. S22, ref 1: remove "Vertiotie.4P" We thank all reviewers for their valuable input that helped improve the manuscript.

Reviewer 1:
General comment: This manuscript presents quantum chemical, statistical rate theory, and flow reactor-mass spectrometric results to establish a new mechanism for the generation of secondary organic aerosol (SOA) precursors in the OH-initiated oxidation of aromatics. The novel reaction being proposed is a concerted rearrangement of bicyclic peroxy radicals in which C-C homolysis, O-O homolysis, and transfer of the H atom from the OH to one of the incipient alkoxy O atoms all happen at one transition state. The manuscript is technically solid, the major results are presented clearly, and the discoveries are highly significant for the area of atmospheric chemistry. I recommend its publication after a few minor issues are addressed: Author comment: We thank the reviewer for their comments and their recommendation for publication of our manuscript. Author comment: We have now increased the font size of the labels in Figure 2.
Changes to manuscript: A larger font size is used for the labels in Fig. 2 of the main manuscript.
2. In the caption to Figure 2, the reference to "P-S2" should probably be to P-C2.
Author comment: Thank you for pointing this out. This has now been corrected.
3. One of the O2 addition barriers reported in Supplementary Section 8 is negative. The same is true in Supplementary Section 2. This does not impede the MESMER simulations based on the quantum chemical data, nor does it render the predicted O2 addition branching ratios invalid. Still, the authors should acknowledge that this is a technical problem that adds uncertainty to the predicted branching ratios.
Author comment: We agree. This is now acknowledged in Supplementary Section 8. Regarding Supplementary Section 2, we suspect that the reviewer is indicating this line in page S6: "This corroborates with the energy barriers for the syn and anti O2 additions we calculated at the F12 level of theory -2.5 kcal/mol and 3.4 kcal/mol, respectively." If so, both barriers are in fact positive (+2.5 kcal/mol and +3.4 kcal/mol), and our use of the hyphen is injudicious here. The hyphen (-) has now been changed to a colon (:) for clarity.
Changes to supplementary: Supplementary Section 8: "Note that the F12 correction causes TSi to be slightly negative, and while this does not impede the MESMER simulations, it does add some uncertainty to the predicted branching ratios". Supplementary section 2, page S6: "-" => ":".
4. On p. 10 and in Figure 4, there is a consideration of "the fastest of the two possible rearrangements for select key aromatics." I am pretty sure that the authors are referring to the rearrangements depicted in Figure 1, but the authors should be explicit about this.
Author comment: We agree that this should be more clearly acknowledged. The text on p. 10 of the main manuscript has been modified to make this clear.
Changes to manuscript: Sentence in p. 10 of the main manuscript changed to: " Fig. 4 shows the rate coefficients of the fastest of the two possible rearrangement mechanisms, C1 and C2 as shown in Fig. 1 A, for select key aromatics." 5. The ends of the two paragraphs in the Atmospheric perspective of the molecular rearrangement mechanism section are somewhat redundant.
Author comment: Thank you for pointing this out, and we agree. We have decided to combine the two paragraphs and modify the last summary sentence.
Changes to manuscript: The two paragraphs in the "Atmospheric perspective of the molecular rearrangement mechanism" section have been combined and this modified final summary sentence has been added: "The novel molecular rearrangement mechanism reported in this work explains the rapid formation of highly oxidized organic products in one of the most important urban SOA-forming systems, toluene + OH, with potential relevance also for other atmospherically abundant aromatic molecules." Reviewer 2: General comment: This manuscript proposed a new rearrangement of ipso-BPRs and also the bicyclic hydroperoxides and nitrates in oxidation of aromatics. The study suggested a new route for formation of highly oxygenated molecules (HOMs) with supports from quantum chemical and kinetic calculations and mass spectrometric observations. Deuterated toluene and D2O were used to probe the reaction pathways and to check the exchangeable protons in the products. Calculations were done at adequate levels, and the experiments were designed carefully to sort support for the proposed mechanism.
The finding here might be a significant improvement on our understanding in mechanism of HOMs and thereafter the mechanism of SOA formation.
Author comment: We thank the reviewer for their comments.
1. # Line 119 "potentially reversible": The reversible H-shifts here should be slow as well, and is much slower than the bimolecular recombination with O2. Therefore should "also be virtually irreversible".
Author comment: In their 2017 paper, Wang et al. (Wang et al. Environ. Sci. Technol. 2017, 51, 15, 8442-8449) report in Table 1 reverse rates for H-migrations in toluene derived BPRs of 1.9´10 6 s -1 and 2.8´10 8 s -1 , which are competitive with bimolecular recombination reactions with O2 under atmospheric conditions. These are for H-migration reactions of BPRs formed from OH additions to ipso and ortho positions, however, and they report virtually irreversible H-migration reactions for the BPR with OH in the para position. We have now modified our text to say that only some of the reported isomerization reactions of BPR are irreversible.
Changes to manuscript: Sentence in the main manuscript modified to: "This is important since some of those previously reported isomerization reactions of BPR, specifically H-shift reactions, were reversible with reverse rate coefficients that are competitive with the bimolecular recombination reactions with O2 under atmospheric conditions." 2. # On reaction of C6H5CD3: There is an issue of isotope effect and tunneling correction here when changing from -CH3 to -CD3. Obviously, the H-shifts here should be much faster than the D-shifts. This might be part of the reason for the low signal for C7D2H6O6 in Fig S11,  Author comment: We agree that the slower -CD3 shift rate could be part of the reason for the observed low C7D2H6O6 signals. If the methyl H-shift was a dominant reaction in our C6H5CH3 measurements and missing in our C6H5CD3 measurements, the observed mass spectra for the two precursors would be expected to be different. However, we observe that the produced mass spectra are near identical (Figs. S12 to S15). We now include the signals of the closed-shell products from the C6H5CH3 experiment (Fig. S11 B) in the supplementary. These signals are also low, indicating that the methyl H-shift is unlikely to play a major role under our experimental conditions. We agree that the isotope effect should nevertheless be noted. We now note it in the manuscript and supplementary text.
Changes to manuscript: We have noted in the manuscript that the use of CD3-toluene might underestimate the role of methyl H-shifts. "Note that D-shift rates are slower than H-shift rates due to isotope effects, in particular lower tunneling factors, so the use of CD3-toluene will to an extent underestimate the role of H-shift from the methyl group. We observe that the mass spectra for toluene and CD3-toluene are near identical, indicating that H-shift from the methyl group is unlikely to play a major role." Changes to supplementary: "While D-shift reactions are known to be slower than H-shifts, and the CD3-toluene experiments could underestimate the role of methyl H-shifts, we also measured low signals of the closed-shell species from the CH3-toluene experiments (Fig. S11  B), indicating that the methyl H-shift is unlikely to play a major role under our experimental conditions." 3. Fig S16, RONO2: BPR + NO forms ROONO first, which might decompose to RO + ONO or isomerize to RONO2. Even though barrier for rearrangement of RONO2 is lower than RO + NO2, the scheme here seems to exaggerate the role of rearrangement. RONO2s were missing in Fig S16 and Table S9. Author comment: We agree that BPR + NO would form ROONO first, that might directly decompose to RO + ONO or isomerize to the more stable RONO2. However, that is not the focus of our work. Our focus is on the eventual fate of the fraction of RO2 + NO reactions that lead to the more stable RONO2 organo nitrate. This is why the PES in Fig. S16 and Table  S9 are missing the ROONO intermediate (we assume that the reviewer meant ROONO and not RONO2 in their comment?). Additionally, we should have noticed (and mentioned) that the rearrangement rates in Table S9 are of thermalized RONO2s as is probably obvious from the rates and the corresponding lifetimes of tens of minutes to hours. We acknowledge that showing the PES in Fig. S16 starting from reactants RO2 + NO without clarifying the lack of role of excess energy in the rearrangement rates is misleading. If excess energy played a role in the rearrangement of RONO2, then we agree with the reviewer that including the ROONO intermediate in the PES would have been necessary. Fortunately, the rearrangement is in fact thermal, and we can therefore avoid computing the complex PES involved in the isomerization of ROONO to RONO2. We now state explicitly that 1) the RONO2 rearrangement reaction is thermal and 2) that the general PES of RO2 + NO includes the ROONO intermediate but is excluded in Fig. S16 and Table S9  4. Presumably, C7H9O9 and C7D2H7O9 were from reaction of C6H5CH3, and C7D3H6O9 and C7D5H4O9 were from reaction of C6H5CD3 (Table S6). So the C7H9O9 contains only two exchangeable H-atoms, insetad "two, three and four" (Page S14). Please confirm or explain.
Author comments: It is correct that the dominant C7H9O9 signal has two exchangeable Hatoms, and we indicate this in the original supplementary text as follows: "Similarly, the proposed autoxidation mechanism points to the C7H9O9 peroxy radical isomer with two acidic functional groups that forms rapidly and is likely the dominant signal. This is corroborated by the D2O experiment." When we note the two, three and four H->D exchanges, it is for the C7H9O11 peroxy radical, as noted in the original supplementary text.
We have now modified the sentence to say 11-oxygen containing C7H9O11 peroxy radical to make it clear that we are talking about the O11 peroxy radical.
Changes to supplementary: In the supplementary, "The D2O experiment also indicates three C7H9O11 peroxy radical isomers with two, three and four H->D exchanges." changed to "The D2O experiments also indicate three isomers for the 11-oxygen containing C7H9O11 peroxy radical with two, three and four H->D exchanges." 5. In Fig 2, three C9H9O9 isomers were given as R3-Epo-OOH-R"O2 (containing one exchangeable H), R2b-OOH-R'2O2 (containing three exchangeable Hs), and the green C7H9O9 (lower left corner, containing two exchangeable Hs). But R2b-OOH-R'2O2 has a fast isomerization rate of ~230 s-1, and the last isomer would have a fast H shift (from the aldehyde H). Alternative isomers of C7H9O9 might be needed to account for the observed signal.
Author comments: We agree that R2b-OOH-R'2O2 is unlikely to accumulate due to its fast isomerization rates. This could at least partially explain why we do not see C7H9O9 isomers with 3 exchangeable H-atoms (see Fig. S14 and S15 where the isomer with 2 exchangeable H atoms is clearly the dominant peak). We also note in the manuscript that we measure C7H9O9 with two exchangeable H-atoms (this sentence is slightly modified to note that the dominant peak corresponding to C7H9O9 has two exchangeable atoms as some small contribution of a peroxy radical isomer with three exchangeable H-atoms cannot be ruled out). It is a good idea to explicitly acknowledge that the blue pathway is not a source of the C7H9O9 peroxy radical exactly for the reason the reviewer suggests. We now note that in the manuscript.
Changes to manuscript: Section Experimental results, 1) "This is more consistent with the mechanism we propose because the formed O9-RO2 via the dominant green pathway in Fig.  2…" 2) "The blue pathway in Fig. 2 does lead to a O9-RO2 with three exchangeable H-atoms, but likely due to its fast isomerization reaction (~230 s -1 ) rapidly forms O11-RO2, and is not measured." 6. Page S14, "… Fig S11 shows the time series of the normalized signals …": The figure cannot be found.
Author comments: Thank you for pointing this out. We initially included and later deleted the time series plot for the D2O experiments, but then neglected to remove our reference to it in the supplementary text. We decided that the figure was too complicated while adding little value. The figure is below: We will remove the reference to the missing figure in the supplementary text. Alternatively, if the reviewer suggests that the plot should be included, we will add it to the supplementary text.
Changes to supplemantary: Removed the reference to Fig. S11 in the supplementary text.
7. Kinetics of R1 (as in Fig S17 and S18): It should be noticed that the two additions of O2 are both reversible, particularly for R1a-RO2 and when R1 contains excess energy. The usual "+ O2 -HO2" process in alpha-hydroxyl alkyl radicals may be limited by the 1,4 H-shift because the addition of O2 to R1a-RO2 is much less exothermic (only ~7 kcal/mol here) than the addition to normal alkyl radicals such as CH3CHOH radical (exothermic by ~30 kcal/mol).
Author comments: We agree that the reversibility of the O2 addition reactions should be noted. The lower exothermicity of the formation of R1a-RO2 will also likely favor the formation of R1b-RO2, making the green channel in Fig. 2 more important. This is now noted in the supplementary text. In addition, we included R1a-RO2 + NO => R1a-ROONO and R1b-RO2 + NO => R1b-ROONO sink reactions with rate coefficients of 1 s -1 to include the reverse reactions of R1a-RO2 and R1b-RO2 in the MESMER simulation. The ROONO was a model system generated without a conformer sampling step and computed at the B3LYP/6-31+G(d) level. The exothermicity of the formation of ROONO was arbitrarily set to -15 kcal/mol relative to the RO2s. If no sink reactions are added and R1a-RO2 and R1b-RO2 are simply treated as "modelled" to account for the reverse reactions, then the product that is thermodynamically the most stable is formed with a 100% yield. Therefore, a sink with an approximately correct timescale to correctly model the effect of reversibility is needed. A more accurate description of the ROONO sink was considered unnecessary as long as the timescale is correct. The rate of conversion of RO2 to ROONO was set at 1 s -1 by giving a NO concentration of 5´10 10 molecules/cm 3 and a reaction rate coefficient of 2´10 -11 cm 3 /molecule/s. This simulation produced a 100% yield of R1b-ROONO, indicating a larger yield of R1b-RO2 when the low exothermicity of R1a-RO2 formation and consequently the reversibility of the two O2 addition reactions are accounted for.
Changes to supplementary: "The formation of all intermediates in Fig. S18 Fig. S19 and the input file is provided in the data archive. This resulted in 100% yield of R1b-ROONO, indicating a larger yield of R1b-RO2 when low exothermicity of R1a-RO2 formation is accounted for." 8. Flow tube simulations: Could typical concentrations of OH radical and RO2 be given here? These quantities are essential in assessing the competition between unimolecular and bimolecular reactions for peroxy radicals.
Author comments: These are now included in the supplementary. The OH concentrations are ~7´10 7 molecules cm -3 and RO2 concentrations are ~9´10 9 -~1´10 10 molecules cm -3 for the flow tube simulations with reaction times of 0.8 s, 1.5 s and 3.7 s.
Changes to supplementary: Typical concentrations of OH radical and RO2 now provided in Fig. S20 in the supplementary.
Changes to supplemenatry: Corrections have been made to the supplementary.
Reviewer 3: General comment: This manuscripts describes a pathway in the atmospheric oxidation of aromatics that appears to be the missing link between the traditional chemistry and the unexplained HOM formation from these compounds. By combining theoretical kinetic calculations, a kinetic model, and experimental observations, the authors make a case that inclusion of this pathway leads to predictions that are consistent with the observations. The research is timely, as there is a lot of interest in HOM and aerosol formation, and the role of aromatics in urban air quality. The methodologies used are of high level and appropriate for the topic, leading to robust results. This paper describes a high-impact result that has the potential to solve a long-standing conundrum. I support publication of this manuscript.
Author comment: We thank the reviewer for their positive comment and their support for the publication of the manuscript.
First main comment: To me, it feels that the authors did not do due diligence to the literature. While I recognize that space and number of references are limited in the main text, the supporting information contains extensive descriptions of mechanistic steps without any referencing at all. Most of this even seems to be based on a single paper (Wang and coworkers), which does not acknowledge the vast effort that the community has put into elucidating aromatics oxidation mechanisms to establish a base upon which the current study can to add its contribution. The paper also generalizes to aromatics beyond toluene, which is certainly not covered by a single reference to Wang et al.
Reviewing the aromatics literature is daunting and I understand that this is not the manuscript to do this in full, but at the very least some key papers should be cited, as well as mechanistic reviews (e.g. Vereecken 2019, Vereecken and Francisco 2012, Atkinson 2003, Calvert 2002. These, and perhaps some additional references to SARs, will also support some of the calculations in the SI that were only done using low-level methodologies. Below, I will not list all places where literature citations are needed, as it is pervasive.
Author comments: We acknowledge that the aromatic oxidation mechanisms in the supplementary should have been better cited. Key papers suggested by the reviewer are now cited where appropriate.
Changes to supplementary: Papers are cited in supplementary. Page S4: "The initial steps of OH addition to toluene is shown in Fig. S4 and have been discussed in detail in previous works (16)(17)(18)(19)." Second main comment: One should be weary about presenting the experiments as proof of the contribution of the characterized pathway. The experiments show that an autoxidation chemistry exists, but does not establish that the molecules observed are those predicted by the theoretical analysis; autoxidation is known to generate many isomers. While the results seems consistent, there remain uncertainties on the theoretical predictions and the experimental observations, and the latter only span a small range of reaction conditions that may be insufficient to discriminate between distinct reaction mechanism. Likewise, the authors do not establish that the proposed mechanism is also consist with the observations available in the literature. Related to this is that, at first glance, the mechanism seems to miss some pathways, or at least does not discuss their contribution as far as I could find. This includes e.g. the reversibility of the epoxidation in R3 (competitive against O2 addition), the H-migration from -OOH to -O-radical in R3 (with a literature rate ~1E10 s-1), or H-scrambling and ring closure in R2b-OOH-R'2O2, all of which represent reactions classes known to be fast. The kinetic calculations also do not seem to account for the impact of fast H-scrambling across OOH/OO groups on the rate coefficient, as well-documented in the literature. It is unclear whether any of this would affect the predictions, but perhaps the mechanism is not fully robust yet.
Author comment: We agree that we must be careful when assigning peaks from experimental spectra to one theoretically predicted mechanism and we acknowledge that the proposed mechanism does not represent the entire autoxidation chemistry of toluene. It is in fact impossible for it to do so given that we have not explored all the autoxidation channels even in the mechanism we propose (i.e., the autoxidation of the P-C1 peroxy radical). Our choice to discuss the experimental results in relation to our mechanism were to 1) offer mechanistic insights on the autoxidation products of toluene + OH we measure that are formed under the rapid reaction time conditions of our experiments, and 2) highlight that multiple autoxidation pathways can occur concurrently, as predicted by our mechanism. Regarding 1) the only experimental observation available in literature carried out under the reaction time conditions that are close to our study is Wang et al. 2017, and we have compared our result to theirs extensively. Our D2O experiments that indicate the number of -OH and -OOH functional groups are not in disagreement with the RO2 isomers from our mechanism, and this adds credence to our mechanism. Regarding 2) This result is non-trivial as no previous work has shown that excess energy from the formation of an RO2 leads to multiple autoxidation pathways. Specifically, the two isomers of O7-RO2, one with one labile H-atom and another with two labile H-atoms shows that multiple autoxidation paths occur concurrently, and this is not in disagreement with the green and red pathways in Fig. 2.
We acknowledge that the proposed pathways provide one explanation and possible structures of the observed highly oxidized RO2s. We agree that there could be other autoxidation pathways not considered in this study that can also lead to the RO2s we detect. This clarification has now been made in the text.
Regarding the red channel in Fig. 2 and the issues the reviewer raises about 1) reversibility of R3-Epo-R' and 2) H-migration from -OOH to -O radical, which is essentially the reverse reaction of R3 back to P-C2. We ran a MESMER simulation along the R1, R2 and R3 pathways of P-C2 with parameters calculated at the wB97X-D/aug-cc-pVTZ level. The lower level of theory is to use the same methodology as what is used for computing the TS to R3 for which CCSD(T)-F12 calculations are unreliable. For R1, we ignored the closed-shell C7H8O5 forming channel and assigned the formation of R1b-RO2 as the direct sink of R1 (+ O2). The simulation shows that R3-Epo-RO2 is a significant product (36% yield). While the reverse reactions have low barriers, the excess energy of P-C2 likely drives the formation of the R3-Epo-R'O2.
Other pathways available to R2b-OOH-R'2O2 such as H-scrambling could be competitive with the vinoxy forming channel shown in Fig. 2, but these do not directly lead to the next O2 addition. The -OH H-atom is likely still very labile, and abstraction of that H-atom by the Hscrambled RO2 would still lead to the same R2b-OOH-vinoxy. The ring closure reactions are unlikely to be competitive with H-shifts from -OH and -OOH groups as our previous calculations, e.g., ring closure reactions of R2a-RO2, indicate that these have much larger barriers. We completely agree with the reviewer that the mechanism is not robust yet. We now make that clear in the manuscript text.
Changes to manuscript: Pg. 5: "R3 and R3-Epo-Rʹ both have small reverse barriers, but the yield of R3-Epo-RO2 is nevertheless likely to be high due to the excess energy of P-C2 as shown in our simulations (see supplementary section S12)." Pg. 5. "Note that autoxidation is known to produce many isomers and the pathways shown in Fig. 2 are not the only autoxidation pathways occurring in our measurements. However, these are the only pathways that can currently explain the observed H-to-D shifts in the isomers we measure." Changes to supplementary: New supplementary section S12 added that describes the favorability of the formation of R3-Epo-RO2.
Minor comments: 1. p. 3 line 79: "finite timescales" define "finite", in this context probably relative to atmospheric transport time scales (regional, continental, hemisphere, global ?) Author comment: Thank you, we agree that the word "finite" is somewhat ambiguous in this context. We have now changed it to regional atmospheric transport timescales.
Changes to manuscript: Pg. 2: "Intriguingly, several of the organo nitrates and other closed shell products derived from the i-BPR are likewise unstable and decompose on regional atmospheric transport timescales."

p. 4 lines 90-105:
This would be significantly easier to understand with a graphical inset with a Lewisstructure representation of an example. Author comment: We have now included a 2-D schematic of the rearrangement reaction in Fig. 1. Changes to manuscript: A 2-D schematic of the rearrangement reaction is included as Fig. 1 A.

p. 5 fig 1:
Top: One can not really see what the rearrangement is, due to the use of ball-andstick graphics. See also remark above. Bottom: Perhaps an Arrhenius plot with x-axis in 1000K/T ? Then again, Nat.Comm is not a kinetics journal.
Author comment: Regarding top: we have now included a 2-D schematic of the rearrangement reaction in Fig. 1 A. Regarding bottom: We decided to show an easier to read temperature relation plot for modelers. The Arrhenius form of the plot is now included in the supplementary (Fig. S22).
Changes to supplementary: The Arrhenius plot of the rearrangement reactions of toluene derived i-BPR is provided in the supplementary (Fig. S22).

p 7 fig 2:
-Caption: "autoxdation" -> autoxidation -The intermediates must not be represented as trans-alkenes but strictly as cisisomers or unspecified (where allylic rotation is possible). Trans-stereoisomers are not what was calculated (sampling a few of the log files shows as much), are not what is expected for the parent molecule decomposition, and would prevent some of the chemistry to happen (e.g. the H-shift in R2b-RO2) -The fates for P-C2 do not sum to 100% Author comment: -Typo in caption corrected.
-The intermediates in Fig. 2 are now represented as cis-isomers.
-The fates of P-C2 should sum up to 79% as the remaining is the yield of P-C1. We acknowledge that this might not be clear from the figure, and we now make a note to this effect in the figure caption.
Changes to manuscript: -Typo corrected.
- Fig. 2 modified to show intermediates as cis-isomers.
-Text added to Fig. 2 caption noting that the yield of P-C2 is 79% and that the fates of P-C2 add up to that. 5. p. 9 line 183: " indicating that the mechanism proposed in this work is the dominant unimolecular pathway to the SOA precursors that we detect." "is" -> is likely to be / is consistent with / ...
Author comment: We agree with the reviewer's correction to this sentence. The text now reads "…indicating that the mechanism proposed in this work is likely to be the dominant unimolecular pathway to the SOA precursors that we detect." Changes to manuscript: The text now reads "…indicating that the mechanism proposed in this work is likely to be the dominant unimolecular pathway to the SOA precursors that we detect."